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Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures

Yves Meyer École Normale Supérieure de Cachan, Cachan, France
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Softcover ISBN: 978-0-8218-2920-2
Product Code: ULECT/22
122 pp
List Price: $32.00 MAA Member Price:$28.80
AMS Member Price: $25.60 Electronic ISBN: 978-1-4704-2169-4 Product Code: ULECT/22.E 122 pp List Price:$30.00
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AMS Member Price: $38.40 Click above image for expanded view Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures Yves Meyer École Normale Supérieure de Cachan, Cachan, France Available Formats:  Softcover ISBN: 978-0-8218-2920-2 Product Code: ULECT/22 122 pp  List Price:$32.00 MAA Member Price: $28.80 AMS Member Price:$25.60
 Electronic ISBN: 978-1-4704-2169-4 Product Code: ULECT/22.E 122 pp
 List Price: $30.00 MAA Member Price:$27.00 AMS Member Price: $24.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$48.00
MAA Member Price: $43.20 AMS Member Price:$38.40
• Book Details

University Lecture Series
Volume: 222001
MSC: Primary 35; 42; 65; 76;

Image compression, the Navier-Stokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective. The notion that unifies the three problems is that of “oscillating patterns”, which are present in many natural images, help to explain nonlinear equations, and are pivotal in studying chirps and frequency-modulated signals.

The first chapter of this book considers image processing, more precisely algorithms of image compression and denoising. This research is motivated in particular by the new standard for compression of still images known as JPEG-2000. The second chapter has new results on the Navier-Stokes and other nonlinear evolution equations. Frequency-modulated signals and their use in the detection of gravitational waves are covered in the final chapter.

In the book, the author describes both what the oscillating patterns are and the mathematics necessary for their analysis. It turns out that this mathematics involves new properties of various Besov-type function spaces and leads to many deep results, including new generalizations of famous Gagliardo-Nirenberg and Poincaré inequalities.

This book is based on the “Dean Jacqueline B. Lewis Memorial Lectures” given by the author at Rutgers University. It can be used either as a textbook in studying applications of wavelets to image processing or as a supplementary resource for studying nonlinear evolution equations or frequency-modulated signals. Most of the material in the book did not appear previously in monograph literature.

Graduate students and researchers working in functional analysis and its applications, in particular to signal and image processing.

• Chapters
• Chapter 1. Still images compression
• Chapter 2. The role of oscillations in some nonlinear PDE’s
• Chapter 3. Frequency modulated signals, chirps and the Virgo program
• Conclusion
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Volume: 222001
MSC: Primary 35; 42; 65; 76;

Image compression, the Navier-Stokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective. The notion that unifies the three problems is that of “oscillating patterns”, which are present in many natural images, help to explain nonlinear equations, and are pivotal in studying chirps and frequency-modulated signals.

The first chapter of this book considers image processing, more precisely algorithms of image compression and denoising. This research is motivated in particular by the new standard for compression of still images known as JPEG-2000. The second chapter has new results on the Navier-Stokes and other nonlinear evolution equations. Frequency-modulated signals and their use in the detection of gravitational waves are covered in the final chapter.

In the book, the author describes both what the oscillating patterns are and the mathematics necessary for their analysis. It turns out that this mathematics involves new properties of various Besov-type function spaces and leads to many deep results, including new generalizations of famous Gagliardo-Nirenberg and Poincaré inequalities.

This book is based on the “Dean Jacqueline B. Lewis Memorial Lectures” given by the author at Rutgers University. It can be used either as a textbook in studying applications of wavelets to image processing or as a supplementary resource for studying nonlinear evolution equations or frequency-modulated signals. Most of the material in the book did not appear previously in monograph literature.